Introduction

This article describes how damage from turrets (guns) are generated in EVE. The information here is focused on concepts and game mechanics. The practical use of this lies mostly in the understanding of how falloff and tracking works, and how far you can push them without loosing any noticeable performance.

All the data is based on facts, drawn from the mathematical equations working behind the scene every time someone pulls a trigger. Since not everyone is fond of math, the article will be divided into two sections. The first part is more like a summary that describes all the concepts and how they work. The second part is just the same thing all over again, but more detailed and with math.

Additional information about turrets can also be found on Turrets and tips and tricks for using turrets more effectively is at Gunnery Guide.

The First Part: Summary

To understand how turret damage is generated you will need to understand a number of concepts and how they interconnect. Some of them are visible under the attributes tab when you click for info on your guns, but not all. Especially the concepts falloff and tracking are easy to misunderstand, angular velocity can be too, so be extra careful when reading those.

Hit chance

A turret always has a 0–100 percent chance to hit a target. The hit chance starts at 100% but factors that reduce the hit chance can lower this. Those factors are basically the range to the target and the target's movement, with a few modifications. When the hit chance has been calculated, the EVE server will "roll a die" for each turret to see if it hits or misses the target. One thing that needs to be emphasized is that your own piloting can change your hit chance, by actively trying to control the range and the movements relative to your opponents.

DPS

DPS stands for Damage Per Second. This number is calculated from the average damage per hit that you do (if your hit chance is 100%) divided by the turret's rate of fire (ROF). The fitting window in the game will show you your DPS from turrets, drones and missiles respectively.

Randomness of damage

The damage from turrets always has a random factor in it, this is built into the game and can't be avoided. Under ideal conditions, when your hit chance is 100%, the damage done by your turrets will be inside an interval of 50% to 150% of your average damage (your target's resistance will reduce the damage done too). However, things are different when your hit chance decreases. Not only will you have a chance to miss your target, which means no damage done. But also, the damage interval will change as well. That interval is actually from 50% but only up to (50% + hit chance). So if your hit chance is 70%, not only will you miss a few shots, the shots that do hit are now in the damage interval of 50% to 120%. There are thus two simultaneous factors that reduce your damage when your chance to hit goes down. (This description has two tiny intentional errors in it that were used to help explain this concept more easily: the first error is that the damage interval is spread around what is known as base damage, the second error is that the percent interval only has 99 units, more details can be found in the second part below).

Perfect hits

In the 0–100 percent hit chance interval, there is a 1% chance of doing a perfect hit. It is that first percent unit in the entire interval. Think of it as rolling a hundred-sided die; if it lands on a 1, you get a perfect hit regardless of the hit chance. This actually means that if your hit chance is a measly two percent, half of your hits will be perfect. If your hit chance is less than one percent, you must first get that hit, before it can become a perfect one. A perfect hit will always do exactly 300% of your base damage.

Range

The distance to the target you are shooting at. Range is used to determine penalties to hit chance based on the distance between the shooter and the target.

Angular velocity

This can be a tricky concept. It describes how fast something passes by something else. It is measured in in radians per second (rad/s), where one radian is equal to about a 57° angle (more accurately, 360° = 2π radians). Your ingame overview can show this value if you open its settings and tick a box under the tab called columns. Angular velocity is used to determine the penalty to the hit chance based on the turret's tracking capabilities. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting). A cool headed player can use special maneuvers (like keep at range) or modules (turning webs on and off can really mess with orbiting ranges) to drastically reduce the angular velocity of a foe to open up for some heavy handed blows against a target that is otherwise hard to track.

Transversal speed

The angular velocity is calculated by dividing the transversal speed by the range to the target (don't mix meters and kilometers if you calculate this, use just meters for both). Transversal speed is sideways speeds, not speeds towards or from the target (that is called radial speed). If you stand on a straight road and see a car coming, the car will have no sideways movement but a large radial movement towards you. If you stand next to the road and watch a car passing you by, the car will have a large sideways movement but almost no radial. High transversal speeds are important for speed tanking, never fly straight towards or away from a target. If you do, the need for tracking drops to zero and you will be shot dead even by the biggest guns.

Optimal

Inside this range the gun will suffer no reduction in hit chance due to distance. If the target is sitting still inside the optimal range, every single attack will hit it.

Falloff

Falloff is an extra range that goes beyond your optimal range. This is, however, not a limit value, like the optimal range is. It is best described as a gradual loss of hit chance, where the given number (plus optimal) represents the distance at which you are down to a 50% hit chance. At two times your falloff value your hit chance is down to 6.25%, even though it is unlikely you can still hit your target at that range, and at three times your falloff range the chance to hit is only 0.2%.

Tracking

Tracking is a value that indicates how well you can hit targets that are passing you by, higher tracking is needed for faster moving targets. This is not a limit value either, in fact it works exactly as falloff does. When the target's angular velocity is equal to the turret's tracking value you will have a 50% hit chance (note: size of the target will also affect this, see below). Just as for falloff, when a target's angular velocity is two times your tracking, the hit chance is down to 6.25%.

Turret Signature Resolution

This value kind of represents the accuracy of the turret. But only kind of, because it will only be important for tracking, it plays no part when it comes to the range. In EVE, every gun can hit the bulls-eye of any target in range regardless of its size as long as it is absolutely still. If the target begins to move, on the other hand, the size suddenly becomes important. All small guns have 40 m as their value, all medium guns have 125 m and all large guns have 400 m. The smaller the better.

Target Signature Radius

It doesn't matter what a ship looks like physically. They are all treated as if they were spheres when they are shot at. The target signature radius describes how big this sphere is, the bigger it is the easier it will be to track with guns. A big target also tend to take more damage from missiles, but that is outside the scope of this article.

Damage loss from Falloff and Tracking

Targets out in falloff, along with targets that must be tracked, are harder to hit. A lower hit chance means less damage done. The real question is, how much less damage? So lets look at that. First of all, one really nice thing with falloff and tracking is that they both behave exactly the same way, so the data table below applies to both of them.

The "Percent of Tracking or Falloff" values means how much of the listed falloff or tracking you are looking at. If your falloff is 12 km then 33.3% means one third of that, so 4 km. If your tracking is 0.4 rad/s then 50% would mean 0.2 rad/s.

Percent ofTracking or Falloff

Hit chance

DPS reduction

0%

100%

0.0%

25%

95.8%

−6.1%

33.3%

92.6%

−10.6%

50%

84.1%

−22.1%

84.8%

60.8%

−50.0%

100%

50.0%

−61.1%

150%

21.0%

−85.2%

200%

6.25%

−94.3%

300%

0.20%

−99.4%

The best performance is up to 1/4 (quarter) of your falloff or tracking, the DPS loss is almost unnoticeable. At 1/2 (half) the DPS reduction is starting to be noticeable but it is still not too bad. Exactly at your falloff or tracking your DPS will be less than half, which is bad. As a rule of thumb, avoid using more than half of your falloff or tracking when you are trying to deal high damage.

Target size

As mentioned above, target size only influence tracking penalties, never range penalties. It may seem counter intuitive, but that is the way the game works. The overview has a column for ship sizes, but those values are not related to a ship's signature size.

The trickiest part with sizes is that you must account for this yourself, the game doesn't help you. The table below is not exact, but gives an idea of how much the size difference will impact the tracking ability of small, medium and large guns.

Adjust your own tracking with these multiples to compensate for size difference

Turretsize

Versus target

Frigate (40 m)

Cruiser (125 m)

Battlecruiser (300 m)

Battleship (400 m)

Small

×1

×3

×7.5

×10

Medium

×0.33

×1

×2.5

×3

Large

×0.10

×0.33

×0.75

×1

Example 1: A battleship with large guns (400 m resolution) fires on a frigate (40 m radius). The weapon attributes tab says the tracking is 0.11 for the fitted guns, but due to the size the actual tracking is now only one tenth of that, so only 0.011.

Example 2: A battlecruiser with medium guns (125 m resolution) fires on a frigate (40 m radius). The tracking value is written as 0.12 rad/s. But medium guns against a frigate means that the tracking is actually down to one third. So the practical tracking value is 0.04 rad/s, due to the size.

Example 3: A cruiser with medium guns (125 m resolution) fires on a battleship (400 m radius). The tracking value is written as 0.12 rad/s. Medium guns against a battleship tracks three times better. So the practical tracking value is 0.36 rad/s.

Grouping guns, does it affect the damage?

No. Even if the guns are grouped on your screen, they are still treated separately. This can be seen by collecting damage data and comparing that with the normal expected damage distribution, it's very clear that it's a combination of several separate turret shots instead of a single one. It can also be deduced by looking at the turret group's damage output when shooting at hard to hit objects, like things deep into falloff, it's possible to tell when one, two or more guns hit the target.

Does a Target Painter help turrets?

Since these modules increases the targets signature size, it means that turrets will have an easier time to track the victim. Increasing your own tracking with, for example, +30% helps just as much as increasing the targets signature size with +30% (stacking penalties will probably be counted separately but this has not been verified). It is noteworthy that a T2 Target Painter with full skills give a +37.5% boost and help your friends tracking too, while a T2 Tracking Computer (with tracking script) gives +30% (but it can swap to increased range scripts, can't miss and need less cap).

The Second Part: Mechanics and equations

The To-Hit-Equation

This equation is used every single time someone fires a turret weapon in the game. The purpose of it is to determine the odds the turret has to hit its target. The value will always be between 0 and 1, or 0% and 100% if you will. The computer then generates a random number to see if a hit is scored or not.
...where:

Angular velocity of target in radians/second. Simply put, how many circles the target can run around you per seconds.

"Weapon Accuracy Score" found on the attributes tab of a turret. For the purposes of keeping track of (and canceling) measurement units, this may be treated as radians/second. The raw number, itself, can also be thought of as "I can hit, half the time, a 40-meter frigate going around me at THIS MANY milliradians per second of angular velocity."

Target signature radius in meters. The size of the target, or more precisely the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.

A math function that takes the highest value of zero or x. It is used to prevent negative values in this case; any negative numbers are replaced with zero instead.

Distance between firing ship and target in meters.

"Turret optimal range" found on the attributes tab of a turret. Inside this range no range penalties from distance are applied. Measured in meters.

"Falloff" found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.

Now let's look a little closer at the equation itself, there is something to be learned from that.

To paraphrase Oli Geist, this equation can be abstracted to

Math students may recognize that something of the form x(a+b) is identical to xaxb, so we can rewrite the above as

Why is this interesting? From this we can see that tracking and range are actually calculated separately, then the results from each are multiplied. This shows that Range and Tracking are indeed two different and independent things, and both will be used to score a hit.

There is also one more thing we can find out by just looking at the equation. This is, however, a little trickier to follow, but the conclusion is easy. The aim is to compare the tracking term and the range term for similarities in how they behave. Do they have anything in common? To do this, we will freeze all values in those respective terms except for one variable in each, that will be 'turret tracking' and 'falloff' respectively. Then we can look at how that single variable effects the outcome in each case and see if there is any similarities between them.

The tracking part: All turrets measure tracking speed as a Turret Accuracy Score, which describes how well a turret can cope with targets moving around the turret in circles (or how well the turret can cope with its own ship moving around the target in circles; as far as the equation is concerned, these are the same situation). Let's freeze the angular velocity, meaning the ships are orbiting each other at a constant speed. In the tracking term we also have a 40000 meters term (a true constant) and target signature radius (which is usually constant except when any effects that affect signature radius are applied or removed). The result: a fixed number divided by turret tracking.

The range part: Being inside optimal never incurs a hit penalty, so we must move out into falloff ranges to see any changes in the to-hit equation's output values. Lets freeze everything apart from falloff. The result: a fixed number divided by falloff.

Did you see what they have in common? In the tracking term, we now have something/Turret tracking, in the range term we have something/falloff. In both cases there is a value that is divided by the variable we were interested in. There is an important insight here: tracking and falloff behave identically. Also, they are not fixed limits, they become ratios that describes how quickly you lose hit chance as you start to push range and orbiting speeds. Also, the hit chance loss is gradual.

Base damage

All turrets have a base damage, this is a fixed number. The volley damage that your turrets do will be spread around this number. The higher the number the more damage the turret will do when it hits. It is calculated from the turret's Damage Multiplier attribute and the ammo's damage values. This is before any resistances are taken into consideration. A high base damage means that your guns hit hard (but do not mistake this for DPS (damage per second) since that also depends on how often the guns may fire). The base damage is always a bit below the average damage (about 1.5% lower) when there is a 100% hit chance because of the rare-but-powerful perfect hits.

Example: A small turret has a damage multiplier of ×1.725, and is loaded with an ammo type that does 7 EM and 5 Thermal damage. The base damage is then 1.725 × (7 + 5) = 20.7.

The random damage distribution

At the heart of a turret's damage output is a single randomly generated value between 0 and 1 that is several digits long, something like 0.317226. This random number is used both to determine if the turret hits the target and then to determine how much damage the hit actually did. Should the randomly generated number be less than 0.01 (1% chance), it will be a perfect hit (aka "wrecking"). A wrecking hit always deals exactly three times the base damage, exactly, there is no random element in damage from perfect hits. The thing about perfect hits is that they always occur as long as that random number was lower than 0.01 and at the same time lower than the hit chance. So perfect hits are not scored by 1% of the shots that can hit, but by 1% of all hits and misses taken together. This means that if your chance to hit is 1% or less, you will either hit perfectly or you will miss, with no normal hits.

The raw damage dealt by a turret is calculated by taking the randomly generated number that resulted in a hit, adding 0.49, and multiplying this sum with the turret's base damage. Since the first 1% of the random value is used for perfect hits, normal hits have a damage spread between 0.50 to 1.49, or 50% to 149% of the base damage, or in the case of perfect hits always exactly 300% of the base damage. This number will then be reduced accordingly by the target's damage resistances in order to obtain the final damage number.

The quality of a non perfect hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage).

Hit description

Random damage modifier

Barely scratches

0.500–0.625

Hits lightly

0.625–0.750

Hits

0.750–1.000

Well aimed

1.000–1.250

Excellent

1.250–1.490

Perfectly

3.000

A turret with a 100% hit chance will see a natural and unavoidable damage spread between 50% to 149% of its base damage for normal hits, and will always do exactly 300% of its base damage on perfect hits. A turret with a 75% hit chance will have a damage spread of 50%–124% on normal hits and do 300% on perfect hits, so with a 75% hit chance there can be no excellent hits because they are now turned into misses.

Example:
A small gatling laser turret fires on target. The chance to hit is 0.8981. The EVE server rolls a random number between 0 and 1, and gets 0.6573—this is less than the chance to hit so the shot lands on the target. At this point 0.49 is added to the random number which then becomes 1.1473. The turret had a damage multiplier of ×2.1 and the ammo does 4 EM and 2 Thermal, so the base damage is 2.1 multiplied with 6 (4+2), which is 12.6. After multiplying this with the random number we get the raw damage, which is 1.1473 × 12.6 = 14.456. This damage will become lower when resistances have been accounted for. In the combat log the hit will be described as "well aimed."

Damage and DPS reduction due to a lower hit chance

When a turret has less than 100% chance to hit the damage is reduced in two different ways. The first and obvious one is that it sometimes misses, the other is that the max damage on normal hits (e.g. not perfect ones) are reduced as well. Both of these effects will decrease the DPS output.

Since it was established earlier that Tracking and Falloff behave exactly the same way. We can use the same data table and the same graphs to describe both, but only one at the time.

The table below shows how damage and DPS goes down as a result of lower hit chance. The decrease is identical for tracking and falloff so either one can be used. If you wish to combine the effects of tracking and falloff, look them up individually and then multiply them (note: this only works for the columns Hit Chance and Relative DPS; the column Reduction in DPS by % can not be used for this).

The true strength with the table and graphs below are not to calculate what your DPS might be in a given situation. But rather to see how much you can push your falloff and tracking while still maintaining a decent DPS output.

Notes: Parts into means the value you multiply either your falloff or your tracking with. 0.25 means 25% or a quarter of that value. Likewise, the hit chance is expressed the same way. The relative DPS is a multiple to the base damage of the turret, it starts above 1 because of the perfect hits, since they do extra high damage.

Tracking upgrades vs Damage upgrades

Weapon upgrade modules can improve raw damage, tracking and range. Making use of an increased range is fairly obvious. However, comparing tracking and damage can be harder to do. The tricky thing with this comparison is that the need for tracking in a fight often varies depending on how the pilots fly their ships. So to make any sense of the following you must have some rough ideas of what the angular velocities will be. The only way to get that is through experience.

Here are some guidelines for comparisons: (note that only the bonus of the 1st module is considered for all tracking modules, additional ones will suffer from a stacking penalty).

Damage Upgrade module, T2 (such as Gyrostabilizer, Heat Sink etc):

The 1st T2 Damage Upgrade module increase damage with +23.5%

The 2nd T2 Damage Upgrade module increase damage with +20%

The 3rd T2 Damage Upgrade module increase damage with +13%

The 4th T2 Damage Upgrade module increase damage with +6.5%

Tracking Enchancer, T2:

When Angular velocity = 25% of your Tracking: +9.5% more tracking is the same as +1.1% damage

When Angular velocity = 50% of your Tracking: +9.5% more tracking is the same as +4.2% damage

When Angular velocity = 75% of your Tracking: +9.5% more tracking is the same as +9.5% damage

When Angular velocity = 100% of your Tracking: +9.5% more tracking is the same as +16.6% damage

Tracking Rig, T1:

When Angular velocity = 25% of your Tracking: +15% more tracking is the same as +1.5% damage

When Angular velocity = 50% of your Tracking: +15% more tracking is the same as +6.3% damage

When Angular velocity = 75% of your Tracking: +15% more tracking is the same as +14.3% damage

When Angular velocity = 100% of your Tracking: +15% more tracking is the same as +25.4% damage

Tracking Computer, T2 with tracking script:

When Angular velocity = 25% of your Tracking: +30% more tracking is the same as +2.7% damage

When Angular velocity = 50% of your Tracking: +30% more tracking is the same as +10.8% damage

When Angular velocity = 75% of your Tracking: +30% more tracking is the same as +25.2% damage

When Angular velocity = 100% of your Tracking: +30% more tracking is the same as +46.7% damage

Target Painter, T2 with Signature Focusing at level IV
(increasing sig radius have the exact same result on damage as an increase in tracking has)

When Angular velocity = 25% of your Tracking: +36% higher sig radius is the same as +3.0% damage

When Angular velocity = 50% of your Tracking: +36% higher sig radius is the same as +12.3% damage

When Angular velocity = 75% of your Tracking: +36% higher sig radius is the same as +28.8% damage

When Angular velocity = 100% of your Tracking: +36% higher sig radius is the same as +54.1% damage

Webs:

The effect from a web is hard to predict, since its use can change both the transversal speed and the range between the ships. Experience and practice will be your best guide here. The drawback with webs is that they can help your opponents tracking as well as your own. The web is more often used for its tactical benefits, such as giving control over the range. But it is also the best tool to reduce the need for tracking when large guns are used against small targets.

Choosing turrets

Is it better with high damage or high tracking turrets? It is almost always better to go for the highest possible damage, which also gives a higher range. This is true for long range (like artillery) and short range (like autocannons) guns alike. The reason for this is because the gain in tracking isn't enough to compete with the lost damage.

The only turret type where higher tracking can possibly outweigh the extra damage and range is for autocannons, the other types simply don't gain enough tracking to be worth even looking into. The lighter autocannon type has +32% tracking, −23% damage and −17% falloff compared to the heavier type (for small, mediums and large alike). The following example will compare heavy vs light, there will be lots of numbers, but there is a summary at the end of it of it all if you want to skip ahead.

Example:This is a comparison of when the lighter type overtakes the heavier type against a target with high angular velocity. For this example it is assumed that that the targets signature radius is identical to the guns signature size, the range is also assumed to be the same in both cases so that the angular velocity will be identical. A pilot is using the heavier autocannons (for example small 200 mm, but this comparison is true for medium and large as well) and is fighting at 0.333 parts into falloff (corresponds to about 2200 m with hard hitting ammo and T2 guns (for T1 it would be 2100 m, so no real difference)), this corresponds to a 10% DPS loss from range, tracking isn't considered yet. If the pilot instead had been using the lighter autocannons (small 125 mm) the range is the same (2200 m for T2 guns) but this time it corresponds to 0.4 parts into falloff where the DPS loss from falloff is 15%. Now we will compare the guns damage output, we must remember that the lighter version does −23% damage as well. So in this range case the relative DPS from the heavier one is 0.90 and for the lighter it is (0.85 × 0.77 =) 0.655, we can divide them (0.9/0.655) to find out that the heavier ones do 37% more DPS over the lighter ones. Now the question is, at how many parts into tracking will these guns do the same damage? Since the lighter ones track better, the heavier ones will lose DPS faster and we are looking for the point where they do the same damage. It turns out that when the heavier type is at 0.9 parts into tracking, they lose 53% DPS, at the same time the lighter version is only 0.68 parts into tracking (0.9/1.32, 32% faster tracking), where it loses 36% DPS. Comparing the relative DPS we get that the lighter do 0.64 and the heavier 0.47, we divide them (0.64/0.47) and see that the lighter ones do 36% more DPS (from just tracking) at this point. This is close to the 37% advantage that the heavier had from before.

Summary: Only when the heavier autocannons get near 1.0 parts of their tracking, will the lighter ones start performing better. At this point, the drop in DPS is already big (like half). It is therefore generally more useful to fit the heaviest type you can and then fly in a way that reduce the demand for tracking if need be. Lighter weapons are mostly only useful when a ship uses up its CPU and PG on other things.

Experiment to determine the damage interval around base damage

This test has too much data to show all of it here, so the method and the results will be presented instead. Should you wish to check for yourself feel free to follow this procedure:

A frigate (named 'Ouch') was abandoned at a safespot. An Osprey was fitted with lasers (infinite ammo, perfect for AFKing), a remote shield transfer and shield transfer drones. The guns and the ammo were chosen so that the damage would never go below 10.0 and to give as large of a damage interval as possible (an interval of at least 10.0 units (resistances must be accounted for) is needed to get a precision of at least 1% in the damage values) -- this ensured that the data would be good enough to draw accurate conclusions. The damage was only done to the shields, they where never allowed to drop below 25% since a bleed through into armor can happen that can mess with the observed damage numbers. Finally, the ships were positioned within optimal range and their speeds set to zero to ensure that the chance to hit is 0.50 = 100% and nothing less.

After 10,656 shots at the poor frigate, enough data was collected to make some conclusions about how the random damage distribution looks like. The data ends up in the My Documents\EVE\gamelogs folder (in Windows), and was easily copied into a prepared Excel sheet for analysis.

Analysis of the data and interpretation of some reduced frequencies of min and max results in the normal damage span:

Of the 10,656 shots the lowest recorded damage was 11.4 (recorded 15 times) and the highest non-perfect was 34.0 (recorded 33 times), perfect hits dealt 68.5 damage (recorded 101 times). On average, each damage number (anything between 11.5 to 33.9) was recorded 46.7 times (standard deviation = 7.02). The reason for the lower occurrences of the min and max results on normal hits comes from rounding effects. Any damage in-between has an interval of 0.1 units (22.2500 to 22.3499 both produce the 22.3 in the log). However the min and max values do not have that span. The lowest theoretical number is Base Damage × 0.5 = 11.415, hence the interval to get 11.4 in the log is between 11.415 and 11.4499, that is only 0.0345 difference. So the expected number of occurrences of the value 11.4 is only 34.6% of the average number, 15 recorded values / 34.6% = 43.4, close to average and inside the standard deviation. The upper interval is 67.8%, 33 times / 67.8% = 48.7, also close to average and inside the standard deviation. (Note: 34.6% + 67.8% = 102.4%, which is of course impossible—the error comes from rounding errors in the 4th decimal of the base damage, awesome precision isn't needed for this comparative calculation since the natural random deviation is much larger anyhow, so this is good enough, the objective was to explain the lower frequencies of the end points which now has been done).

Lowest damage random multiple

Modified base damage × 0.51 = 11.6

Modified base damage × 0.50 = 11.4

Modified base damage × 0.49 = 11.2

The lowest observed damage is 11.4, thus 50%

Highest non-perfect random multiple

Modified base damage × 1.50 = 34.2

Modified base damage × 1.49 = 34.0

Modified base damage × 1.48 = 33.8

The highest non-perfect damage is 34.0, thus 149%

Perfect hits deal 68.5 damage

Modified base damage × 3 = 68.5

The collected data shows that the normal damage is distributed within 50%–149%. Since the first 1% unit is used for critical rolls (this is most likely, if the last % unit was used additional calculations will be needed if the to hit chance is less than 1%), the constant added to the damage roll should be 0.49.